How is adaptive subdivision different from dynamic topology?
The difference between Adaptive subdivision and Dynamic topology is the way the surface gets subdivided. Both triangulate the mesh but use different algorithms. 

Adaptive subdivision:




each polygon is divided into a number of micro-polygons based on camera distance and screen pixel size
these micro-polygons are displaced at render-time with texture
the subdivision algorithm makes it easy to increase/decrease the density
resulting triangles are nice (a quad results in smaller quads that form 2 triangles each)


Dynamic topology:




the division algorithm divides the mesh based on brush size while sculpting the mesh
the created vertices are created at their final destination
decreasing/increasing resolution is done by collapsing/subdividing edges locally with brushes and globally in tool panel under Dyntopo settings
local subdivision and collapsing of edges usually create nasty geometry with long thin triangles and triangle fans.